A degenerate elliptic system with variable exponents
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We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived; in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results.
Keywordsdegenerate elliptic systems degenerate p(x)-Laplacian operator weak solutions weighted variable exponent spaces mountain pass lemma
MSC(2010)35J70 35J20 35J25 35J92 46E35
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This work was supported in part by a University of Tennessee at Chattanooga SimCenter-Center of Excellence in Applied Computational Science and Engineering (CEACSE) grant.
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